A campus police officer shot and killed the president of a gay and transgender student group outside a Georgia Tech dormitory in Atlanta on Sunday. A cellphone video shared widely online showed the student, who was believed to be holding a knife, yelling “shoot me” at the officers before one opened fire.

The student, Scout Schultz, 21, died at a local hospital from a single gunshot wound, according to a statement by the Georgia Bureau of Investigation, which is investigating the altercation.

The killing, which happened in full view of students in the dormitory, immediately raised questions about why the campus police were so quick to use deadly force.

After what the university called a peaceful vigil for Schultz on Monday night at Georgia Tech, about 50 people marched to the campus Police Department, where a police car was set on fire and two officers received minor injuries, the authorities said. Three people were arrested on charges of inciting a riot and battery of an officer. At one point, the university urged students to stay inside because of the violence.

The statement released earlier by the Bureau of Investigation referred to Schultz as male. According to the website of the Georgia Tech Pride Alliance, the student identified as “bisexual, nonbinary, and intersex” and used the pronoun “they.” Intersex is a condition in which a person’s physical sex characteristics do not align with typical notions of male and female.

It was Schultz who called 911 to report a suspicious white male with long blonde hair on campus holding a knife and possibly a gun, the Georgia Bureau of Investigation said. After the shooting, investigators found three suicide notes in the student’s dorm room, the agency said.

In an interview with The Atlanta Journal-Constitution, Lynne Schultz, the student’s mother, asked why the police were so quick to kill her child, who she said suffered from depression and had attempted suicide in the past.

“Why didn’t they use some nonlethal force, like pepper spray or Tasers?” Ms. Schultz asked the paper.

Lance Wallace, a university spokesman, said Georgia Tech campus police do not carry Tasers but they do carry pepper spray. L. Chris Stewart, a lawyer for the Schultz family, criticized the university for not providing officers with more nonlethal tools and said the killing would not have happened if campus police officers were properly trained to handle mental illness.

“From the video you can see Scout is in the middle of the mental breakdown and telling the officers to shoot,” he said. “Four of them did not listen to that and continued to do their job, to de-escalate the situation, but one of them decided to take Scout’s life.”

“If someone says shoot me or writes a letter or whatever it is, you don’t assist them with that,” he added.

Mr. Wallace said he was not able to answer questions about the killing on Monday, although he did say the campus police had not shot anyone on campus “in at least 20 years and perhaps never.”

The episode began before midnight on Saturday when the campus police received the 911 call at 11:17 p.m., according to a statement from the Georgia Bureau of Investigation.

The video of the shooting appears to show Schultz with hands hanging down, holding no apparent weapon, though officers can be heard referring to a knife. The Georgia Bureau of Investigation said one multipurpose tool was found at the scene of the shooting. Its blade was not extended, according to The Journal-Constitution.

The video that was shared online and broadcast on cable news showed the student ambling down the street in front of a parking garage toward two police officers with their guns drawn.

The campus officers can be heard several times ordering Schultz to drop a knife. “Nobody wants to hurt you,” one officer said. Another asked, “What’s going on, man?”

At two points the student could be heard saying, “Shoot me!”

A third officer’s voice can be heard telling Schultz not to move, and the student responded by walking toward that officer.

Shortly after that a single shot was fired, followed by the sound of anguished screaming. The university has not released the name of the officer who fired that shot.

It was not clear how long the entire encounter lasted.

The university said on Monday that it had sent a text alert to students at 11:32 p.m. to report “a campus emergency in progress” and to advise them to find shelter and “lock all doors and windows.” At 11:50 p.m. students received a second text: “There is no longer a threat to campus.”

In an email sent to the university community on Sunday morning, John Stein, a dean, mourned the student’s “sudden and tragic death” but did not disclose to students and faculty that it was campus police who had killed the fourth-year engineering student from Lilburn, Ga.

The dean said the death was “devastating news for the Schultz family, classmates, and for members of the community who knew Scout personally, the shock and grief are particularly acute.”

Pride Alliance, the lesbian, gay, bisexual and transgender student group at Georgia Tech, said in a statement that Schultz was the group’s “driving force” for the past two years.

“We would not be the organization we are known as without their constant hard work and dedication,” the group said, using the slain student’s preferred pronoun. “We love you Scout, and we will continue to push for change.”

Correction:Sept. 18, 2017

An earlier version of this article misspelled the hometown of a Georgia Tech student who was killed over the weekend. The student was from Lilburn, Ga., not Liliburn.